The Menu — The Choice, Plate viii

The deepest defense ever offered of rational choice is that its central requirement asks nothing about the world. A person's preferences may be anything at all — noble or base, wise or foolish, this set of tastes or its mirror — and the theory does not mind; it asks only that her choices, whatever drives them, be consistent with one another. Take the same option from a large menu that you took from a small one containing it; do not choose A over B and then, from the same offerings, B over A. These are conditions on the choices alone, referring to nothing outside them — not to feelings, not to welfare, not to the reasons behind the picking. That is their glory, as their defenders see it: rationality made purely internal, a matter of the choices hanging together, checkable from the behavioral record without any inquiry into the chooser's mind or her circumstances. The argument of this plate, which belongs to Amartya Sen, is that the internality is an illusion — that the consistency conditions cannot so much as be stated without a substantive assumption about the world, and that the assumption is false.¹

1. The internal-consistency program runs from Samuelson's weak axiom (1938) through Houthakker (1950) to Arrow's treatment of choice functions (Rational Choice Functions and Orderings, 1959), with its conditions on how a chooser's selections must cohere across menus — the best known being the contraction property (often Property α): anything chosen from a set must be chosen from every subset of that set in which it still appears. Sen develops the critique across Behaviour and the Concept of Preference (1973), Internal Consistency of Choice (Econometrica, 1993), and Maximization and the Act of Choice (Econometrica, 1997).

Sen's demonstrations are small domestic scenes, and their plainness is part of their force. Consider a basket holding one large apple and one small. A guest, offered the basket, takes the small apple and leaves the large — an ordinary courtesy; one does not take the best of what little there is. Now enlarge the basket: the same large apple, but two small ones beside it. From this menu the guest might feel free to take the large, since a small one remains for whoever comes after. Suppose she does. Then she has chosen the large apple when the menu held three, yet declined it when the menu held only the large and one small — and that is a violation of the contraction property, the very heart of internal consistency: an option chosen from the bigger set was refused from a subset of it. By the formal standard she has been irrational. By every human standard she has behaved perfectly. The resolution is not subtle, which is the point: what she was choosing among was never apples. It was apple-takings — acts of taking-this-apple-from-this-company — and the act of taking the larger apple means a different thing when it strips the basket bare than when it leaves a share for others. The menu did not merely present the options; it set what choosing each of them would amount to.²

2. The example and its kin appear in Sen (1993). The contraction property is breached not by any inconsistency in the guest's reasons — which hold perfectly steady: be courteous — but by the theory's insistence on describing the objects of choice as the apples themselves rather than as the acts of taking them in their setting.

A second scene makes a different cut. A person invited to a stranger's home for tea is offered, simply, tea; she accepts, preferring tea to nothing. On another visit the same host offers a choice between tea and a line of cocaine; now she declines the tea and takes nothing at all. She has chosen tea over nothing in the first instance and nothing over tea in the second — again, formally, a reversal of preference between the two occasions. But nothing about the tea has altered. What has altered is what the menu has told her. A host who lays out cocaine beside the tea is a different prospect from a host who offers tea alone, and the mere presence of the unchosen option has revised her sense of where she is and with whom — has, reasonably, made her wish to accept nothing from this person at all. The rejected alternative did its work without being chosen, by informing her. This is the epistemic value of the menu: the set of things on offer is itself a message, and a chooser who reads the message and acts on it is responding to information, not contradicting herself.³

3. Sen (1997). The scene dramatizes that the choice set carries information about the world — the chooser infers, from what is offered, something about the offerer and the situation — so that two choices made from differently composed menus are not choices made under the same conditions, and the consistency requirements, which assume that they are, simply misdescribe the case.

⁂

Generalize from the scenes and the thesis stands clear. The consistency conditions treat the menu as an inert container — a neutral list from which a selection is drawn, contributing nothing to the meaning of the selection. But the menu is not inert. The options present, the options absent, the social setting, the meaning carried by the act of taking this rather than that — all of these are part of what is chosen over, and a description of choice that keeps only the bare selections has thrown that part away. Once it is gone, behavior that was entirely reasonable looks inconsistent, because the information that would have made it intelligible is exactly the information the formalism declined to keep. A reader of the companion volume will recognize the shape of this argument, for it is the same shape exactly. There, the comparison of one person's welfare with another's proved impossible not for want of measurement but because the discipline had discarded the psychological substance a comparison would have needed, in the very act of making utility rigorous.⁴ Here, the internal consistency of one person's choices proves undefinable not for want of data but because the discipline has discarded the context a judgment of consistency would have needed, in the very act of making choice purely behavioral. In both, the rigor was real and the cost identical: a quantity emptied of the only content that would have let it do the work it was built for. The figure and the ground have traded places. The menu — the supposed background, against which the real event, the choice, was to stand out — turns out to carry the meaning the theory had located in the choice. To choose is not to point at an option. It is to perform an act whose sense the whole situation supplies.⁵

4. See № 08, The Utility, plate viii (The Comparison). The parallel is exact, and within this series deliberate: two foundational projects — interpersonal comparison and internal consistency — each fail not through a technical shortfall but because the information that would have sustained them was discarded as the price of rigor.

5. Sen's name for choice that takes the menu's meaning into account is the act of choice, as against the mere outcome chosen; the 1997 title, Maximization and the Act of Choice, marks the distinction. Maximization over outcomes is well defined; the act of choosing carries, in addition, the meaning of having chosen thus, from these.

There is a way to save the formalism, and it is the same way that was offered, and found wanting, in the plate on reversals. One may insist that the guest was not inconsistent because she was never choosing among apples but among context-laden apple-acts; that the tea-drinker reversed nothing, tea-from-a-cocaine-offering-host being a different good from tea-from-an-ordinary-host. Re-describe the options finely enough — fold the whole context into the specification of each alternative — and consistency is restored, every time, for any behavior whatever. The move is formally unanswerable. It is also self-defeating, for it secures consistency by surrendering content. If the objects of choice may be re-individuated without limit whenever an inconsistency threatens, then the consistency conditions forbid nothing: no pattern of behavior could ever breach them, since any apparent breach would be redescribed into a choice among different goods. A requirement that nothing could fail is not a requirement. The theory may keep its axioms or it may keep its bite; the re-description rescue is the price of the first, paid in the second. And the choice between them is not a technicality but a confession of what the theory was for. An internal standard, checkable from behavior alone, was the entire promise — and that promise cannot be kept once the context must be written into every option to keep the books straight, because the context is precisely what is not in the behavioral record.⁶⁷

6. Unrestricted re-description of the options is the choice-theoretic analogue of fitting a curve through any data by adding parameters at will. Arrow–Debreu state-contingent commodities — a good indexed by the state of the world in which it is delivered — are a disciplined, economically motivated use of fine individuation; the rescue under discussion is the undisciplined use, individuation introduced after the fact, solely to absorb a violation.

7. The dilemma is Sen's: a theory of choice can be internal, its consistency defined over bare selections, or it can be substantive, its consistency defined relative to the chooser's reasons and the meanings of acts — but it cannot be both, because the substantive content needed to make consistency reasonable is exactly the content that internality forswears.

⁂

What remains of rational choice once the menu has been admitted? Not nothing, and it is worth being exact about the residue, since the temptation is to read the argument as more destructive than it is. The reasonable behavior in Sen's scenes was not random; it was governed throughout by stable reasons — be courteous, do not take the last of a scarce good, accept nothing from a person who deals in cocaine. What fails is not the idea that choice answers to reasons but the idea that the reasons can be reconstructed from the bare pattern of selections, without inquiry into what the chooser was doing and why. The replacement Sen proposes is a reason-based account: choice is rational when it tracks the agent's reasons, and those reasons routinely reach past the option to the menu, the context, and the meaning of the act of taking. This is a more honest and a more demanding standard, and it gives up something the discipline had prized: it cannot be applied from the outside, by an observer holding only the choice data, because the data underdetermine the reasons. The dream that made choice the unshakeable floor of economics — a rationality one could certify from behavior alone, needing to know nothing of the person — does not survive. The floor was level, it turns out, only because the room had been cleared of everything that gives a choice its meaning.⁸

8. Reason-based and norm-sensitive reconstructions of rationality are pursued by Sen and others — see also the work on choice under social norms gathered in the companion element № 26, The Norm. The cost is the loss of an external, behavior-only test of rationality: reasons must be interpreted, not merely recorded, and interpretation reaches past the data the internal program had confined itself to.

It is worth marking where this leaves the volume's larger argument, since the eighth plate here was written as a companion to the eighth plate of The Utility, and the two are meant to be read as one. That plate showed the want behind a price dissolving into the choice that was supposed to reveal it. This one shows that the choice will not, in its turn, stand on its own — that it is not the self-contained, context-free act the theory required, but a performance whose meaning the surrounding world must supply. Where the volume travels from here is to follow choice out past the single chooser altogether: into the divided self whose preferences will not hold still, into the freedom that added options confer and the burden they lay on, and at last back to the want it began by replacing. But the load-bearing result is already in hand. The floor beneath choice is not solid. It was only ever the floor of a cleared room.